Many investors were hopeful that the new president would focus renewed energy on tackling deteriorating economic conditions in America -- a vital export market for Asian goods -- that have dragged on growth around the world.
The relief that came with the end of the U.S. election was an added boost to sentiment, which has improved on the belief that, as the credit crunch eases, world equities markets could see a year-end rally after October's brutal sell-off.
Obama's win "is an excuse for the market to rally. There's less political uncertainty and that gives investors more confidence in the short term," said Frank Gong, a Hong Kong-based managing director for JP Morgan Securities. "But technically it's more about the credit crisis settling down and the market's fear coming down."
Some analysts said the next administration would be hard pressed to deliver a quick fix to the many U.S. economic woes.
"Changing the president is not going to be enough to save the American economy," said Kazuo Mizuno, chief economist at Mitsubishi UFJ Securities Co. in Tokyo.
He said the U.S. is likely to need financing from Japan, China, the Middle East and other countries if it hopes to fund public bailouts for its financial system and deliver on tax breaks and other measures needed for recovery.
"Even the president is not going to be able to change America without help from the world," Mizuno said.
Most markets across Asia markets rose. Japan's Nikkei 225 stock average advanced 4.5 percent to 9,521.24, and Hong Kong's Hang Seng Index surged 5.2 percent to 15,126.69.
Australia's index rose 2.9 percent, and Singapore's key stock measure added 4.4 percent. India's market fell 1.9 percent.
The upswing followed Wall Street, where many investors looked past more signs of a slumping U.S. economy and piled into stocks.
The Dow Jones index staged its biggest Election Day rally ever, rising 305.45 points, or 3.3 percent, to close at 9,625.28. The broader indices also rose, with the Standard & Poor's 500 index up 39.45, or 4.1 percent, to 1,005.75, its first close over the 1,000 mark since Oct. 13.
Wall Street futures were up modestly, suggesting a higher open in the U.S. Wednesday. Dow futures were up 22 points, or 0.2 percent, at 9,609.
In Japan, a weaker yen boosted shares of major exporters including automakers and consumer electronics firms. Toyota Motor Corp. rose 8.1 percent, Canon Inc. jumped 11.7 percent and Sony Corp. advanced 6.3 percent.
The dollar was trading at 99.70 yen, up from the 98-yen zone the previous day in Asia.
Sanyo Electric Co. surged 18 percent after being untraded Tuesday due to a rush of buy orders triggered by weekend reports that the company may be bought by rival Panasonic Corp.
A Sanyo-Panasonic entity would create Japan's biggest electronics maker, surpassing Hitachi Ltd., and would also be among the biggest in the world. Officials from both companies denied Tuesday that any deal has been reached.
Oil prices retreated after surging above $70 a barrel overnight. Light, sweet crude for December delivery was changing hands at $68.93, down $1.60 cents, in Asian trade on the New York Mercantile Exchange.
Tuesday in Europe, Britain's FTSE 100 index rose 196.22 points, or 4.4 percent, to 4,639.50, while Germany's DAX gained 251.20 points, or 5.0 percent, at 5,278.04. France's CAC-40 jumped 163.12 points, or 4.6 percent, at 3,691.09.